12-267/Homework Assignment 5 - Revision history

Dongwoo.kang at 02:05, 14 December 2012

2012-12-14T02:05:17Z

← Older revision		Revision as of 22:05, 13 December 2012
Line 38:		Line 38:

	[http://imgur.com/a/txF9Z#0 Solutions] [[User:Vsbdthrsh\|Vsbdthrsh]]		[http://imgur.com/a/txF9Z#0 Solutions] [[User:Vsbdthrsh\|Vsbdthrsh]]


			Solutions to HW5: [[User:Dongwoo.kang\|Dongwoo.kang]]
			<gallery>
			Image:12-267(HW5-1).jpg\|page 1
			Image:12-267(HW5-2).jpg\|page 2
			Image:12-267(HW5-3).jpg\|page 3
			Image:12-267(HW5-4.jpg\|page 4
			Image:12-267(HW5-5.jpg\|page 5
			Image:12-267(HW5-6.jpg\|page 6
			Image:12-267(HW5-7.jpg\|page 7
			Image:12-267(HW5-8.jpg\|page 8
			Image:12-267(HW5-9.jpg\|page 9
			Image:12-267(HW5-10.jpg\|page 10
			Image:12-267(HW5-11.jpg\|page 11
			Image:12-267(HW5-12.jpg\|page 12
			Image:12-267(HW5-13.jpg\|page 13
			</gallery>

Vsbdthrsh at 21:53, 7 November 2012

2012-11-07T21:53:59Z

← Older revision		Revision as of 17:53, 7 November 2012
Line 34:		Line 34:

	(Here, of course, <math>e^D:=\sum_{k=0}^\infty \frac{D^k}{k!}</math>).		(Here, of course, <math>e^D:=\sum_{k=0}^\infty \frac{D^k}{k!}</math>).

			{{Template:12-267:Dror/Students Divider}}

			[http://imgur.com/a/txF9Z#0 Solutions] [[User:Vsbdthrsh\|Vsbdthrsh]]

Drorbn at 10:25, 2 November 2012

2012-11-02T10:25:18Z

← Older revision		Revision as of 06:25, 2 November 2012
Line 1:		Line 1:
	{{12-267/Navigation}}		{{12-267/Navigation}}

	This assignment is due at ~~the tutorial~~ on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.		This assignment is due in class on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

	'''Task 1.''' Consider the following systems of equations:		'''Task 1.''' Consider the following systems of equations:

Drorbn at 21:21, 31 October 2012

2012-10-31T21:21:05Z

← Older revision		Revision as of 17:21, 31 October 2012
Line 32:		Line 32:

	'''Task 3.''' Let <math>D</math> be the differential operator <math>\frac{d}{dx}</math>, and let <math>f</math> be a function of the variable <math>x</math> whose Taylor series is convergent everywhere. Write a simple formula for <math>(e^Df)(x)</math>.		'''Task 3.''' Let <math>D</math> be the differential operator <math>\frac{d}{dx}</math>, and let <math>f</math> be a function of the variable <math>x</math> whose Taylor series is convergent everywhere. Write a simple formula for <math>(e^Df)(x)</math>.

			(Here, of course, <math>e^D:=\sum_{k=0}^\infty \frac{D^k}{k!}</math>).

Drorbn at 15:10, 29 October 2012

2012-10-29T15:10:13Z

← Older revision		Revision as of 11:10, 29 October 2012
Line 1:		Line 1:
	{{12-267/Navigation}}		{{12-267/Navigation}}
	{{In Preparation}}

	This assignment is due at the tutorial on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.		This assignment is due at the tutorial on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

Drorbn at 17:41, 26 October 2012

2012-10-26T17:41:48Z

← Older revision		Revision as of 13:41, 26 October 2012
Line 4:		Line 4:
	This assignment is due at the tutorial on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.		This assignment is due at the tutorial on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

	'''Task 1.'''		'''Task 1.''' Consider the following systems of equations:

			<math>A:\begin{cases}
			\dot{x}=x-2y & x(0)=3\\
			\dot{y}=4y-2x & y(0)=1\\
			\end{cases}</math>

			<math>B:\begin{cases}
			\dot{x}=x-5y & x(0)=3\\
			\dot{y}=2x-5y & y(0)=1
			\end{cases}</math>

			<math>C:\begin{cases}
			\dot{x}=y & x(0)=1 \\
			\dot{y}=z & y(0)=2 \\
			\dot{z}=-6x-11y-6z & z(0)=-1
			\end{cases}</math>

			# Write each one in a matrix form.
			# Find the eigenvalues and eigenvectors of the resulting matrices.
			# Diagonalize these matrices.
			# Compute <math>e^{tA}</math> for each of those matrices.
			# Solve these equations.

			'''Task 2.'''
			# Prove that if two matrices <math>A</math> and <math>B</math> satisfy <math>AB=BA</math>, then <math>e^{A+B}=e^Ae^B</math>.
			# Find an example for two matrices <math>A</math> and <math>B</math> for which <math>e^{A+B}\neq e^Ae^B</math>.

			'''Task 3.''' Let <math>D</math> be the differential operator <math>\frac{d}{dx}</math>, and let <math>f</math> be a function of the variable <math>x</math> whose Taylor series is convergent everywhere. Write a simple formula for <math>(e^Df)(x)</math>.

Drorbn at 17:58, 25 October 2012

2012-10-25T17:58:59Z

← Older revision		Revision as of 13:58, 25 October 2012
Line 2:		Line 2:
	{{In Preparation}}		{{In Preparation}}

	This assignment is due at the tutorial on ~~Tuesday~~ ~~October~~ 30. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.		This assignment is due at the tutorial on Friday November 2. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

	'''Task 1.'''		'''Task 1.'''

Drorbn at 02:35, 23 October 2012

2012-10-23T02:35:18Z

New page

{{12-267/Navigation}}
{{In Preparation}}

This assignment is due at the tutorial on Tuesday October 30. Here and everywhere, '''neatness counts!!''' You may be brilliant and you may mean just the right things, but if your readers have a hard time deciphering your work they will give up and assume it is wrong.

'''Task 1.'''

← Older revision		Revision as of 22:05, 13 December 2012
Line 38:		Line 38:

	[http://imgur.com/a/txF9Z#0 Solutions] [[User:Vsbdthrsh\|Vsbdthrsh]]		[http://imgur.com/a/txF9Z#0 Solutions] [[User:Vsbdthrsh\|Vsbdthrsh]]


			Solutions to HW5: [[User:Dongwoo.kang\|Dongwoo.kang]]
			<gallery>
			Image:12-267(HW5-1).jpg\|page 1
			Image:12-267(HW5-2).jpg\|page 2
			Image:12-267(HW5-3).jpg\|page 3
			Image:12-267(HW5-4.jpg\|page 4
			Image:12-267(HW5-5.jpg\|page 5
			Image:12-267(HW5-6.jpg\|page 6
			Image:12-267(HW5-7.jpg\|page 7
			Image:12-267(HW5-8.jpg\|page 8
			Image:12-267(HW5-9.jpg\|page 9
			Image:12-267(HW5-10.jpg\|page 10
			Image:12-267(HW5-11.jpg\|page 11
			Image:12-267(HW5-12.jpg\|page 12
			Image:12-267(HW5-13.jpg\|page 13
			</gallery>